%matplotlib inline

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from matplotlib import cm

import ipyparallel as ipp

from time import time
from datetime import datetime

import motif as mf

from sklearn.model_selection import GridSearchCV, RandomizedSearchCV
from sklearn.decomposition import PCA
from sklearn.utils import shuffle
from sklearn.metrics import mean_absolute_error
from sklearn.metrics import roc_curve, roc_auc_score
from sklearn.model_selection import train_test_split, cross_val_score, cross_validate

from scipy.stats import spearmanr
from scipy.stats import pearsonr

Intel(R) Extension for Scikit-learn* enabled (https://github.com/intel/scikit-learn-intelex)

### set parameters for the motif analysis

PROTEIN_NAME = 'A2PB1'
PROT_CONC = 0.002  # free protein concentration at binding reation; PBM typically 0.1 and RNACompete typically 0.002
BOTH_STRANDS = False  # wheter both strands are present for binding; True if double-stranded DNA or RNA is used as probes
TIME_DISS = 1800  # experimental time span after binding reaction during which dissociation of the protein from the probe was possible

STAGES=mf.stage(protein=PROTEIN_NAME)

### read data

## RNAcompete sample data
dfprobes_raw=pd.read_excel('./data/RNAcompete/A2BP1.xlsx')
#dfprobes_raw=pd.read_excel('./data/RNAcompete/HNRNPA1.xlsx')
#dfprobes_raw=pd.read_excel('./data/RNAcompete/PTBP1.xlsx')
#dfprobes_raw=pd.read_excel('./data/RNAcompete/RBM24.xlsx')


#dfprobes_raw=pd.read_csv('./data/samplePBMs/Mlx__pTH2882_HK.raw', sep='\t')
#dfprobes_raw=pd.read_csv('./data/samplePBMs/Klf9__pTH2353_HK.raw', sep='\t')
#dfprobes_raw=pd.read_csv('./data/samplePBMs/Prdm11__pTH3455_HK.raw', sep='\t')
#dfprobes_raw=pd.read_csv('./data/samplePBMs/Sox10__pTH1729_HK.raw', sep='\t')


print('Columns of imported Data File: %s' % dfprobes_raw.columns)
#dfprobes_raw.describe()
#dfprobes_raw.info()

Columns of imported Data File: Index(['Probe_Set', 'RNA_Seq', 'Probe_ID', 'raw', 'norm'], dtype='object')

### select columns for probe sequence and signal

column_sequence = 'RNA_Seq'
column_signal = 'norm'
#background_signal = 'mean_background_intensity'  #set to None if not needed
background_signal=None

#basic preprocessing
dfprobes_raw[column_signal] = dfprobes_raw[column_signal].apply(
    lambda a: np.NaN if a == ' ' else a)
dfprobes_raw[column_signal] = dfprobes_raw[column_signal].apply(
    lambda a: np.NaN if a == '' else a)
dfprobes_raw[column_sequence] = dfprobes_raw[column_sequence].apply(
    lambda a: np.NaN if str(a).lower() == 'nan' else a)
dfprobes_raw[column_sequence] = dfprobes_raw[column_sequence].apply(
    lambda a: np.NaN if a == '' else a)
dfprobes_raw = dfprobes_raw.dropna()

#construct new dataframe with only necessary data
if type(background_signal) == type(None):
    dfprobes = pd.DataFrame({
        'seq':
        dfprobes_raw[column_sequence].astype(str),
        'signal binding':
        dfprobes_raw[column_signal].astype(np.float32)
    })  #rebuild dataframe
else:
    dfprobes = pd.DataFrame({
        'seq':
        dfprobes_raw[column_sequence].astype(str),
        'signal':
        dfprobes_raw[column_signal].astype(np.float32),
        'background':
        dfprobes_raw[background_signal].astype(np.float32)
    })  #rebuild dataframe
    dfprobes['signal binding'] = dfprobes['signal'] - dfprobes['background']

dfprobes = dfprobes.dropna()    

    
# display main properties of data set
dfprobes['signal binding'].plot(figsize=(15, 5))
dfprobes.describe()

### check type of nucleic acid

dfprobes['seq'] = dfprobes['seq'].apply(
    lambda seq: seq.upper().replace(" ", ""))  #upper and remove blanks
dfprobes['RNA'] = dfprobes['seq'].apply(
    lambda seq: all(char in 'ACGU' for char in seq))
dfprobes['DNA'] = dfprobes['seq'].apply(
    lambda seq: all(char in 'ACGT' for char in seq))
non_RNA_counts = len(dfprobes[dfprobes['RNA'] == False])
non_DNA_counts = len(dfprobes[dfprobes['DNA'] == False])

if non_RNA_counts < non_DNA_counts:
    NUC_TYPE = 'RNA'
    print('I: RNA probes detected!')
else:
    NUC_TYPE = 'DNA'
    print('I: DNA probes detected!')

if NUC_TYPE == 'RNA' and non_RNA_counts != 0:
    print(
        'E: The probe sequences appear to be RNA, however there are some non-RNA nucleotides in the sequences.'
    )
    print('E: Please check the following sequnces %s' %
          dfprobes[dfprobes['RNA'] == False])

if NUC_TYPE == 'DNA' and non_DNA_counts != 0:
    print(
        'E: The probe sequences appear to be RNA, however there are some non-RNA nucleotides in the sequences.'
    )
    print('E: Please check the following sequnces %s' %
          dfprobes[dfprobes['DNA'] == False])

I: RNA probes detected!

### option to add a constant sequence at the 3' end and 5' end
sequence_to_be_added_5 = ''
sequence_to_be_added_3 = ''  # standard PBM arrays: CCTGTGTGAAATTGTTATCCGCTCT T7 array: GTCTTGA..
dfprobes['seq'] = sequence_to_be_added_5.upper(
) + dfprobes['seq'] + sequence_to_be_added_3.upper()
print(
    f"I: The nucleotide sequence {sequence_to_be_added_5.upper()} has been added to the 5' end all probe sequences."
)
print(
    f"I: The nucleotide sequence {sequence_to_be_added_3.upper()} has been added to the 3' end all probe sequences."
)

I: The nucleotide sequence  has been added to the 5' end all probe sequences.
I: The nucleotide sequence  has been added to the 3' end all probe sequences.

### egalize length
dfprobes['seq_length'] = dfprobes['seq'].apply(len)

if max(dfprobes['seq_length']) != min(dfprobes['seq_length']):
    print('I: Probes length is not uniform, detected range: %i ..%i' %
          (min(dfprobes['seq_length']), max(dfprobes['seq_length'])))
    max_length = max(dfprobes['seq_length'])
    dfprobes['padded_sequence'] = dfprobes['seq'].apply(
        lambda seq: seq + ((max_length - len(seq)) * '-'))
    print(
        "I: Probe sequences have been padded at the 5' to the uniform length of %i nucleotides"
        % max_length)
else:
    print('I: Probe sequences have the uniform length of %i nucleotides' %
          (dfprobes['seq_length'].median()))
    dfprobes['padded_sequence'] = dfprobes['seq']

print('I: Total datasets contains %i sequences.' % len(dfprobes))

# visualize composition of each position
df_nucleotides = mf.split_sequence_in_nucleotides(dfprobes['padded_sequence'])
dfcount = pd.DataFrame(index=['A', 'C', 'G', 'T', 'U', '-'])
for column in df_nucleotides:
    dfcount[column] = df_nucleotides[column].value_counts()
dfcount = dfcount.fillna(0)  #zeros for NaN
dfcount.transpose().plot(figsize=(15, 5), kind='bar')
print('I: Visualisation of the base composition per position')
print(
    'I: If positions are invariant they can be removed before sequence analysis.'
)

I: Probes length is not uniform, detected range: 30 ..41
I: Probe sequences have been padded at the 5' to the uniform length of 41 nucleotides
I: Total datasets contains 241319 sequences.
I: Visualisation of the base composition per position
I: If positions are invariant they can be removed before sequence analysis.

# You may remove invariant continuos positions by adjusting the slicing.
# It is recommended to leave a few invariant positions to allow for binding events
# between the variable and constant part of the probes.

dfprobes['padded_sequence'] = dfprobes['padded_sequence'].apply(lambda s: s[:])  ### <==== do the slicing here

# visualize composition of each position
print('I: Visualisation of the base composition per position after slicing.')
df_nucleotides = mf.split_sequence_in_nucleotides(dfprobes['padded_sequence'])
dfcount = pd.DataFrame(index=['A', 'C', 'G', 'T', 'U', '-'])
for column in df_nucleotides:
    dfcount[column] = df_nucleotides[column].value_counts()
dfcount = dfcount.fillna(0)  #zeros for NaN
dfcount.transpose().plot(figsize=(15, 5), kind='bar')
plt.show()

# preparation for later classification
mean = dfprobes['signal binding'].mean()
std = dfprobes['signal binding'].std()
THRESHOLD = mean + 4 * std  #4*std used according to Weirauch et al., 2013
dfprobes['positive probe'] = dfprobes['signal binding'].apply(
    lambda s: True if s > THRESHOLD else False)

print(
    'I: The whole dataset has been used to set the threshold for a positive probe.'
)
print('I: The threshold is %f' % THRESHOLD)
print(
    f"I: {len(dfprobes[dfprobes['positive probe']])} probes of {len(dfprobes)} are above threshold."
)

if len(dfprobes[dfprobes['positive probe']]) == 0:
    print(
        'E: No probe above THRESHOLD. Classification is not possible. Please adjust the THRESHOLD.'
    )

I: Visualisation of the base composition per position after slicing.

I: The whole dataset has been used to set the threshold for a positive probe.
I: The threshold is 38.582768
I: 1951 probes of 241319 are above threshold.

### Shuffle and prepare dataset for training and testing

# shuffle and split
dfprobes = shuffle(dfprobes)
dftrain, dftest = train_test_split(dfprobes, test_size=0.2)

print(
    'I: The whole dataset has been split in training (80%) and test (20%) datasets.'
)

# display histogramms of test and training set
dftrain['signal binding'].plot(kind='hist', bins=25).axvline(x=THRESHOLD, color='r', linestyle='-.', lw=0.5, label='threshold classification')
dftest['signal binding'].plot(kind='hist', bins=25)
plt.show()

# generate a subset with maximal 1000 probes

downsampled_size = 1000  # You may change downsampled size here.

percentile = 0.5 * downsampled_size / len(
    dftrain
) * 100  #percentile required for lowest and highest to achieve down-sampled size
if percentile < 4:
    percentile = 4  #do not use only the extreme values
elif percentile > 10:
    percentile = 10  #avoid taking value from the mid-range

if len(dftrain) * percentile * 2 / 100 < downsampled_size / 4:
    print('W: The subset only contains %i probes - a rather low number.' %
          dftrain * percentile * 2 / 100)

print(
    'I: A downsampled dataset containing the lowest and highest %.1f %% of the dataset is generated.'
    % percentile)
dfsubset_high = dftrain[dftrain['signal binding'] >= dftrain['signal binding'].quantile(1 - percentile / 100)]  # highest part
dfsubset_low = dftrain[dftrain['signal binding'] <= dftrain['signal binding'].quantile(percentile / 100)]  # lowest part
print('I: Median values of lowest and highest %.1f %%:  %r  %r' %
      (percentile, dfsubset_low['signal binding'].quantile(0.5),
       dfsubset_high['signal binding'].quantile(0.5)))

if len(dfsubset_high) + len(dfsubset_low) > downsampled_size:
    print('I: The dataset is further downsampled to %i sequences.' %
          downsampled_size)
    dfsubset_high = dfsubset_high.sample(downsampled_size - int(downsampled_size / 2))
    dfsubset_low = dfsubset_low.sample(int(downsampled_size / 2))
    dfsubset = pd.concat([dfsubset_high, dfsubset_low])
else:
    dfsubset = pd.concat([dfsubset_high, dfsubset_low])

dfsubset = shuffle(dfsubset)   
    
# display main properties of downsampled data set
print('I: Histogramm of the downsampled dataset along the with classification threshold.')
dfsubset['signal binding'].plot(kind='hist', bins=25).axvline(x=THRESHOLD, color='r', linestyle='-.', lw=0.5, label='threshold classification')
plt.show()

# establish numpy arrays of the sequenc and binding data in the dataframes

# complete data
X=mf.hotencode_sequence(dfprobes['padded_sequence'], nuc_type=NUC_TYPE)
y=np.array(dfprobes['signal binding'])

# training set
X_train=mf.hotencode_sequence(dftrain['padded_sequence'], nuc_type=NUC_TYPE)
y_train=np.array(dftrain['signal binding'])

# subset of training set
X_subset=mf.hotencode_sequence(dfsubset['padded_sequence'], nuc_type=NUC_TYPE)
y_subset=np.array(dfsubset['signal binding'])

# test set
X_test=mf.hotencode_sequence(dftest['padded_sequence'], nuc_type=NUC_TYPE)
y_test=np.array(dftest['signal binding'])

I: The whole dataset has been split in training (80%) and test (20%) datasets.

I: A downsampled dataset containing the lowest and highest 4.0 % of the dataset is generated.
I: Median values of lowest and highest 4.0 %:  -1.2877190113067627  17.646547317504883
I: The dataset is further downsampled to 1000 sequences.
I: Histogramm of the downsampled dataset along the with classification threshold.

### perform a quick & dirty round for a short motif by fitting on subset to check data integrity

#fit regression quick_model
quick_model=mf.findmotif(motif_length=3, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS, ftol=0.01)

start = time()
quick_model.fit(X_subset,y_subset)
print("I: Optimization took %.2f hours." % ((time() - start)/3600))

# print & display main results
quick_model.analyse_motif(X_subset,y_subset, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('quick', quick_model)
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

I: Optimization took 0.04 hours.
I: energy matrix and logos:

       A     C      G     U
0 -2768   854   2189  -275
1  1443  -684   2010 -2769
2  4796  2497 -12287  4994

I: summed absolute energies of each position:
0     6087
1     6908
2    24575
dtype: int64

I: averaged summed energy over all positions: 12523
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -21164 +/- 7370
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00115 .. 0.06661 (ratio: 58.1)
I: number of probes: 1000
I: Pearson Correlation  r: 0.3619
I: mean absolute error: 14.2241

I: Classification performance AUROC: 0.7541

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.06661	0.001147	-2768,..	suppressed

#### Perfrom GridCV Search for exploration of the motif length goal: identify the minimum motif length which gives a good r-value

# optional: allow for global optimization to verify whether the local optimization is good enough
# not recommended include fitG0=True. This option should only be considered when the local optimization is started with an approximate motif and the start parameter is set
# not recommended set time_dissociation. The effect of dissociation should be only considered when the local optimization is started with an approximate motif.


# prepare grid search over motif_length
model_grid=mf.findmotif(protein_conc=PROT_CONC, both_strands=BOTH_STRANDS)
param_grid = {"motif_length": [3,4,5,6,7]}     # choose sensible range for length of motif

# define custom refit function
def custom_refit(cv_results):
    """returns index of max r2/sqrt(motif_length)"""
    df_grid=pd.DataFrame(cv_results)
    index=(df_grid['mean_test_score']/(df_grid['param_motif_length'].apply(float).apply(np.sqrt))).idxmax()
    return index

# run grid search and refit according to custom refit
grid_search = GridSearchCV(model_grid, param_grid=param_grid, verbose=2, cv=5, refit=custom_refit, n_jobs=-1)

start = time()
grid_search.fit(X_subset, y_subset)

print("I: GridSearchCV took %.2f hours for %d candidate parameter settings."
    % ((time() - start)/3600, len(grid_search.cv_results_["params"])))
print('I: number of samples: %i' %len(X_subset))

df_grid=pd.DataFrame(grid_search.cv_results_)
print('I: Plot of r2 vs motif length and vs root(motif length)')
df_grid.rename(columns={'mean_test_score':'r2'}, inplace=True)
df_grid.plot(kind='scatter', x='param_motif_length', y='r2', yerr='std_test_score', figsize=(5,3)).set_xticks(param_grid["motif_length"])
df_grid['r2/sqrt(length)']=df_grid['r2']/(df_grid['param_motif_length'].apply(float).apply(np.sqrt))
df_grid['std/sqrt(length)']=df_grid['std_test_score']/(df_grid['param_motif_length'].apply(float).apply(np.sqrt))
df_grid.plot(kind='scatter', x='param_motif_length', y='r2/sqrt(length)',yerr='std/sqrt(length)', figsize=(5,3)).set_xticks(param_grid["motif_length"])
plt.show()

best_index=df_grid['r2/sqrt(length)'].idxmax()
CORE_MOTIF_LENGTH=df_grid.loc[best_index, 'param_motif_length']
print(f'I: The maximum ({CORE_MOTIF_LENGTH}) is suggested as CORE_MOTIF_LENGTH')

print('I: motif obtained with the best estimator from gridCV search')
# print & display results from best estimator
model_grid=grid_search.best_estimator_
model_grid.analyse_motif(X_subset,y_subset, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('best grid', model_grid)
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

Fitting 5 folds for each of 5 candidates, totalling 25 fits
I: GridSearchCV took 0.92 hours for 5 candidate parameter settings.
I: number of samples: 1000
I: Plot of r2 vs motif length and vs root(motif length)

I: The maximum (5) is suggested as CORE_MOTIF_LENGTH
I: motif obtained with the best estimator from gridCV search
I: energy matrix and logos:

        A      C      G      U
0    950  -3443    910   1582
1  -8527  15252  -3778  -2946
2  14078 -12560  15915 -17433
3   2372   4054  -5973   -454
4    410  -1003  -1331   1924

I: summed absolute energies of each position:
0     6886
1    30504
2    59988
3    12855
4     4669
dtype: int64

I: averaged summed energy over all positions: 22980
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -14587 +/- 17669
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.01146 .. 1.61839 (ratio: 141.2)
I: number of probes: 1000
I: Pearson Correlation  r: 0.4693
I: mean absolute error: 13.5720

I: Classification performance AUROC: 0.8329

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed

### run a number of identical optimizations with motif length found during grid search
### goal: find best motif through repetition, judge stabiltiy of optimization

#CORE_MOTIF_LENGTH=5  # adjust core motif length if needed, motif length can be changed later

# prepare for ipyparallel
number_of_optimizations = 20
model_list = [mf.findmotif(motif_length=CORE_MOTIF_LENGTH, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS)] * number_of_optimizations
X_list = [X_subset] * number_of_optimizations
y_list = [y_subset] * number_of_optimizations


def single_job(model, X, y):
    model.fit(X, y)
    return {'model':model}

# run the optimizations on ipp.cluster
start = time()
with ipp.Cluster(log_level=40) as rc:
    rc[:].use_pickle()
    view = rc.load_balanced_view()
    asyncresult = view.map_async(single_job, model_list, X_list, y_list)
    asyncresult.wait_interactive()
    result = asyncresult.get()
print("I: Optimization took %.2f hours." % ((time() - start) / 3600))


  
# assemble results and analyze
df_repetitions=pd.DataFrame(result)
df_repetitions['r (subset)']=df_repetitions['model'].apply(lambda e: e.rvalue)
df_repetitions['r (train)']=df_repetitions['model'].apply(lambda e: mf.linregress(e.predict(X_train),y_train).rvalue)
df_repetitions['r (test)']=df_repetitions['model'].apply(lambda e: mf.linregress(e.predict(X_test),y_test).rvalue)
df_repetitions['G0']=df_repetitions['model'].apply(lambda e: e.finalG0_)
df_repetitions['max binding']=df_repetitions['model'].apply(lambda e: e.max_binding_fit)
df_repetitions['min binding']=df_repetitions['model'].apply(lambda e: e.min_binding_fit)
df_repetitions['ratio'] = df_repetitions['model'].apply(lambda e: e.ratio)
df_repetitions['energies']=df_repetitions['model'].apply(lambda e: e.energies_)
#df_repetitions['information']=df_repetitions['model'].apply(lambda e: mf.energies2information(e.energies_))


# display results of the ensemble of optimizations
print('I: Results of the repeated motif finding, sorted according to the regression coefficient with the train dataset')
df_repetitions.sort_values('r (train)', ascending=False, inplace=True)
mf.display_df(df_repetitions, nuc_type=NUC_TYPE)

  0%|          | 0/16 [00:00<?, ?engine/s]

single_job:   0%|          | 0/20 [00:00<?, ?tasks/s]

I: Optimization took 0.41 hours.
I: Results of the repeated motif finding, sorted according to the regression coefficient with the train dataset

	model	r (subset)	r (train)	r (test)	G0	max binding	min binding	ratio	energies	logo
4	suppressed	0.627475	0.383789	0.382056	-14468.149919	0.002283	0.000071	32.193670	-1444,..
2	suppressed	0.627094	0.382312	0.380357	-14468.149919	0.042820	0.000899	47.637275	-7956,..
18	suppressed	0.623820	0.381985	0.379701	-14468.149919	0.085601	0.000577	148.373748	13917,..
16	suppressed	0.621807	0.378718	0.375553	-14468.149919	1.112775	0.002003	555.660703	15255,..
14	suppressed	0.622187	0.378541	0.374634	-14468.149919	0.722316	0.004071	177.450826	8038,..
15	suppressed	0.620717	0.378123	0.375699	-14468.149919	0.769708	0.002394	321.511787	9018,..
12	suppressed	0.622048	0.377367	0.373532	-14468.149919	0.997724	0.004769	209.223824	6993,..
19	suppressed	0.621762	0.376560	0.373886	-14468.149919	1.180335	0.002461	479.529779	9588,..
5	suppressed	0.621139	0.375967	0.372101	-14468.149919	1.185211	0.002578	459.812090	12508,..
6	suppressed	0.589723	0.364937	0.359804	-14468.149919	0.904499	0.000781	1157.880476	312,..
0	suppressed	0.559729	0.262107	0.257468	-14468.149919	0.549866	0.000680	809.168322	271,..
1	suppressed	0.474093	0.231931	0.219083	-14468.149919	0.003534	0.000121	29.269731	269,..
8	suppressed	0.471106	0.227495	0.215328	-14468.149919	0.454449	0.003447	131.833480	395,..
7	suppressed	0.462297	0.212451	0.200649	-14468.149919	2.147407	0.000711	3021.633547	1931,..
13	suppressed	0.446330	0.203647	0.204619	-14468.149919	2.048640	0.012393	165.299940	-6072,..
17	suppressed	0.449187	0.193391	0.192369	-14468.149919	9.019759	0.101190	89.136525	473,..
10	suppressed	0.453970	0.193372	0.199473	-14468.149919	4.106599	0.000491	8355.336140	-6297,..
11	suppressed	0.454276	0.179471	0.177296	-14468.149919	8.661975	0.111170	77.916715	3154,..
9	suppressed	0.401516	0.177459	0.169380	-14468.149919	6.934439	0.019933	347.884427	-8821,..
3	suppressed	0.433586	0.174696	0.176083	-14468.149919	3.893036	0.003602	1080.943307	29,..

### compare energy matrices of ensemble using PCA
print('I: Histogram of the regression coefficients r obtained by repeated optimizaion with the subset.')
df_repetitions['r (subset)'].plot(kind='hist')
plt.show()

pca = PCA(n_components=2)
pca_2c=pca.fit_transform(df_repetitions['energies'].tolist())    
df_repetitions[['PCA1', 'PCA2']]=pca_2c
print('I: 2-dimensional PCA explained %i %% of variance.' %(sum(pca.explained_variance_ratio_)*100))
if sum(pca.explained_variance_ratio_)<0.5:
      print('W: 2-dimensional PCA explained only %i %% of variance' %(sum(pca.explained_variance_ratio_)*100))

print('I: Visualization of the PCA with the regression quality vs. subset and training dataset by color.')        
df_repetitions.plot(x='PCA1', y='PCA2', kind='scatter', c='r (subset)',cmap=cm.coolwarm, edgecolors='black', linewidths=0.3)
df_repetitions.plot(x='PCA1', y='PCA2', kind='scatter', c='r (train)',cmap=cm.coolwarm, edgecolors='black', linewidths=0.3)

I: Histogram of the regression coefficients r obtained by repeated optimizaion with the subset.

I: 2-dimensional PCA explained 67 % of variance.
I: Visualization of the PCA with the regression quality vs. subset and training dataset by color.

/home/GLipps/.local/lib/python3.8/site-packages/sklearn/utils/deprecation.py:101: FutureWarning: Attribute `n_features_` was deprecated in version 1.2 and will be removed in 1.4. Use `n_features_in_` instead.
  warnings.warn(msg, category=FutureWarning)

<matplotlib.axes._subplots.AxesSubplot at 0x7f6d6c195310>

# visualisation of the motif with the highest r with the train dataset
print('I: Best motif according to r (train) from the repeated optimizations.')
print('I: PCA components: %i, %i' %(df_repetitions.iloc[0]['PCA1'], df_repetitions.iloc[0]['PCA2']))
model_best_repetition=df_repetitions.iloc[0]['model']
model_best_repetition.analyse_motif(X_subset,y_subset, THRESHOLD, nuc_type=NUC_TYPE) 
# store results and display stages
STAGES.append('best repetition', model_best_repetition, new_entries={'r (test)': mf.linregress(model_best_repetition.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

I: Best motif according to r (train) from the repeated optimizations.
I: PCA components: 6335, -1677
I: energy matrix and logos:

       A     C     G     U
0 -1444   -47 -7531  9023
1   -60 -2983  1492  1551
2 -2579   920  1015   642
3  1864 -1118  2526 -3272
4  1167   570 -2222   485

I: summed absolute energies of each position:
0    18047
1     6087
2     5158
3     8781
4     4445
dtype: int64

I: averaged summed energy over all positions: 8504
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -14671 +/- 6913
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00007 .. 0.00228 (ratio: 32.2)
I: number of probes: 1000
I: Pearson Correlation  r: 0.6275
I: mean absolute error: 11.1763

I: Classification performance AUROC: 0.8929

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo	r (test)
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed		NaN
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed		NaN
2	best repetition	A2PB1	1000	5	0.627475	0.892899	-14468.149919	False	32.193670	0.002283	0.000071	-1444,..	suppressed		0.382056

### motif finding on complete training dataset starting with best motif from repetitions

#fit & predict optimization starting with previous energy matrix
model_train=mf.findmotif(motif_length=CORE_MOTIF_LENGTH, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS,
                   start=model_best_repetition.energies_)
start = time()
model_train.fit(X_train,y_train)
print("I: Optimization took %.2f hours." % ((time() - start)/3600))

# print & display main results
model_train.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('train dataset', model_train, new_entries={'r (test)': mf.linregress(model_train.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

I: Optimization took 10.64 hours.
I: energy matrix and logos:

       A     C     G     U
0   511   208 -6992  6271
1  -121 -3459  1200  2380
2 -3846  1205  1850   790
3  2945 -1092  2349 -4202
4  1716  1439 -4323  1168

I: summed absolute energies of each position:
0    13984
1     7162
2     7693
3    10589
4     8647
dtype: int64

I: averaged summed energy over all positions: 9615
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -14698 +/- 6544
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00004 .. 0.01650 (ratio: 394.2)
I: number of probes: 193055
I: Pearson Correlation  r: 0.4088
I: mean absolute error: 2.7151

I: Classification performance AUROC: 0.9577

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo	r (test)
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed		NaN
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed		NaN
2	best repetition	A2PB1	1000	5	0.627475	0.892899	-14468.149919	False	32.193670	0.002283	0.000071	-1444,..	suppressed		0.382056
3	train dataset	A2PB1	193055	5	0.408764	0.957661	-14468.149919	False	394.225913	0.016499	0.000042	511,..	suppressed		0.409149

### Based on the motif of CORE_MOTIF_LENGTH analyze the neigbouring positions 
### whether their inclusion can improve the quality of the motif
df_positions=model_train.investigate_extension_parallel(X_train,y_train, end5=3, end3=3, nuc_type=NUC_TYPE)

list_positions=df_positions.index[df_positions['+2%']].tolist()+[0] # list of positions with an increase of2% and default position 0
ext5=-min(list_positions)
ext3=max(list_positions)
print("I: It is suggested to extend the core motif at the 5' end by %i and at the 3' end by %i positions." %(ext5, ext3))

  0%|          | 0/6 [00:00<?, ?engine/s]

job5:   0%|          | 0/3 [00:00<?, ?tasks/s]

job3:   0%|          | 0/3 [00:00<?, ?tasks/s]

I: Optimization took 1.31 hours.

I: It is suggested to extend the core motif at the 5' end by 1 and at the 3' end by 0 positions.

### fit & predict optimization starting with extended energy matrix if extension appears to improve prediction

if ext5+ext3!=0: #extension suggestion from previous analysis of the bordering positions
    expanded_energies=model_train.energies_
    # append energies of single-optimized bordering positions to energies of central part
    if ext5!=0:
        energies_5=np.concatenate(df_positions['energies'][(df_positions.index<0) & (df_positions.index>=-ext5)].to_numpy())
        expanded_energies=np.concatenate((energies_5, expanded_energies))
    if ext3!=0:
        energies_3=np.concatenate(df_positions['energies'][(df_positions.index<=ext3) & (df_positions.index>0)].to_numpy().flatten())
        expanded_energies=np.concatenate((expanded_energies,  energies_3))

    mf.energies2logo(expanded_energies, nuc_type=NUC_TYPE)
    print('I: Optimization started with following extended motif.')
    expanded_motif_length=len(expanded_energies)//4
    
    
    model_extended=mf.findmotif(motif_length=expanded_motif_length, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS,
                   start=expanded_energies)

    start = time()
    model_extended.fit(X_train,y_train)
    print("Optimization took %.2f hours." % ((time() - start)/3600))

    # print & display main results
    model_extended.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

    # store results and display stages
    STAGES.append('train, extended', model_extended, new_entries={'r (test)': mf.linregress(model_extended.predict(X_test),y_test).rvalue})
    mf.display_df(STAGES.df, nuc_type=NUC_TYPE)
else:
    print('I: Motif is not extended based on previous analysis.')

I: Optimization started with following extended motif.
Optimization took 8.11 hours.
I: energy matrix and logos:

       A     C     G     U
0  -330   698   758 -1126
1  2279  1101 -8292  4911
2    23 -3731  1255  2452
3 -4009  1317  1898   793
4  2787 -1141  2386 -4032
5  1626  1394 -4244  1222

I: summed absolute energies of each position:
0     2914
1    16585
2     7462
3     8018
4    10348
5     8488
dtype: int64

I: averaged summed energy over all positions: 8969
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -11859 +/- 6889
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00001 .. 0.01293 (ratio: 1132.2)
I: number of probes: 193055
I: Pearson Correlation  r: 0.4295
I: mean absolute error: 2.6935

I: Classification performance AUROC: 0.9608

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo	r (test)
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed		NaN
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed		NaN
2	best repetition	A2PB1	1000	5	0.627475	0.892899	-14468.149919	False	32.193670	0.002283	0.000071	-1444,..	suppressed		0.382056
3	train dataset	A2PB1	193055	5	0.408764	0.957661	-14468.149919	False	394.225913	0.016499	0.000042	511,..	suppressed		0.409149
4	train, extended	A2PB1	193055	6	0.429464	0.960805	-11634.110305	False	1132.198714	0.012935	0.000011	-330,..	suppressed		0.438725

### fit & predict optimization starting with extended energy matrix plus one bordering position on each side if current bordering position exceed the information of 0.25

last_model=STAGES.df.at[max(STAGES.df.index),'model']   
I_5=mf.energies2information(last_model.energies_[0:4])>=0.25 #sufficient information content of 5' end position
I_3=mf.energies2information(last_model.energies_[-4:])>=0.25 #sufficient information content of 3' end position

if I_5 or I_3:
    print('I: At least one of the bordering positions of the current motif has an information content of at least 0.25. Extending.')
    expanded_energies_with_border=mf.modify_energies(last_model.energies_, end5=I_5, end3=I_3)  
    mf.energies2logo(expanded_energies_with_border, nuc_type=NUC_TYPE)
    motif_length_with_border=len(expanded_energies_with_border)//4

    model_with_border=mf.findmotif(motif_length=motif_length_with_border, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS,
                   start=expanded_energies_with_border)


    start = time()
    model_with_border.fit(X_train,y_train)
    print("Optimization took %.2f hours." % ((time() - start)/3600))

    # print & display main results
    model_with_border.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

    # store results and display stages
    STAGES.append('train, expanded, border', model_with_border, new_entries={'r (test)': mf.linregress(model_with_border.predict(X_test),y_test).rvalue})
    mf.display_df(STAGES.df, nuc_type=NUC_TYPE)
else:
    print('I: Both bordering positions of the found motif have an information content below 0.25. No futher optimization required.')

I: At least one of the bordering positions of the current motif has an information content of at least 0.25. Extending.

Optimization took 9.68 hours.
I: energy matrix and logos:

       A     C     G     U
0  -346   704   776 -1134
1  2190   978 -8528  5359
2    32 -3714  1263  2418
3 -4040  1355  1893   792
4  2868 -1174  2401 -4095
5  1629  1389 -4319  1299
6   -17  -362   125   254

I: summed absolute energies of each position:
0     2960
1    17056
2     7428
3     8081
4    10541
5     8638
6      759
dtype: int64

I: averaged summed energy over all positions: 7923
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -9270 +/- 7123
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00000 .. 0.00612 (ratio: 1439.4)
I: number of probes: 193055
I: Pearson Correlation  r: 0.4315
I: mean absolute error: 2.6865

I: Classification performance AUROC: 0.9603

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo	r (test)
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed		NaN
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed		NaN
2	best repetition	A2PB1	1000	5	0.627475	0.892899	-14468.149919	False	32.193670	0.002283	0.000071	-1444,..	suppressed		0.382056
3	train dataset	A2PB1	193055	5	0.408764	0.957661	-14468.149919	False	394.225913	0.016499	0.000042	511,..	suppressed		0.409149
4	train, extended	A2PB1	193055	6	0.429464	0.960805	-11634.110305	False	1132.198714	0.012935	0.000011	-330,..	suppressed		0.438725
5	train, expanded, border	A2PB1	193055	7	0.431486	0.960336	-9027.941911	False	1439.405725	0.006122	0.000004	-346,..	suppressed		0.437049

last_model=STAGES.df.at[max(STAGES.df.index),'model']  
df_relevant_positions=last_model.explore_positions(X_train, y_train)
list_positions=df_relevant_positions.index[df_relevant_positions['-2%']].tolist() # list of positions with an increase of2% and default position 0
start_relevant=min(list_positions)
end_relevant=max(list_positions)
red5=-start_relevant
red3=end_relevant-len(df_relevant_positions)+1
print('I: The analysis suggests, that positions between %i to %i contribute significantly to the motif' %(start_relevant, end_relevant))
last_model=STAGES.df.at[max(STAGES.df.index),'model']

if (end_relevant-start_relevant+1)in STAGES.df['motif length'].to_list():
    print('I: No need for a further optimization. An optimization with motif length of %i has already been done.' %(end_relevant-start_relevant+1))
    print('I: Checking whether G0 has been chosen correctly.')
    last_model.investigate_G0(X_train, y_train)
else:
    print('I: Bordering positions only marginally contributing towards regression quality are dropped.')
    print('I: New start energy for motif optimization:')
    start_final_model=mf.modify_energies(last_model.energies_, end5=red5, end3=red3)
    mf.energies2logo(start_final_model, nuc_type=NUC_TYPE)
    final_model=mf.findmotif(motif_length=len(start_final_model)//4, protein_conc=PROT_CONC, 
                             both_strands=BOTH_STRANDS, start=start_final_model)

    start = time()
    final_model.fit(X_train,y_train)
    print("Optimization took %.2f hours." % ((time() - start)/3600))

    # print & display main results
    final_model.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)
    
    print('I: Checking whether G0 has been chosen correctly.')
    final_model.investigate_G0(X_train, y_train)

    # store results and display stages
    STAGES.append('train, shrinked', final_model, new_entries={'r (test)': mf.linregress(final_model.predict(X_test),y_test).rvalue})
    mf.display_df(STAGES.df, nuc_type=NUC_TYPE)  

I: The analysis suggests, that positions between 0 to 5 contribute significantly to the motif
I: No need for a further optimization. An optimization with motif length of 6 has already been done.
I: Checking whether G0 has been chosen correctly.
I: Current G0 = -9028 J/mol (see red broken line in figure below) with r = 0.431.
I: Maximal r is 0.431 at G0=19972 J/mol (see green broken line below).
I: Maximal occupancy of 2 is reached at G0=-27028 J/mol (see blue broken line below).
I: Maximal occupancy of 0.2 is reached at G0=-18028 J/mol (see blue broken line below).

W: Current G0 leads to a maximal probe occupancy below 0.2. G0 can be manuylly set and be decreased.
I: Maximal r is close to r achieved with current G0. Good.

### optional adjustment of GO

G0=-15000   # <==== adjust G0 manually here

last_model=STAGES.df.at[4,'model'] # <==== select appropiate model
last_model.G0=G0

start = time()
last_model.fit(X_train,y_train)
print("Optimization took %.2f hours." % ((time() - start)/3600))

# print & display main results
last_model.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('manually adjusted G0', last_model, new_entries={'r (test)': mf.linregress(last_model.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

Optimization took 8.40 hours.
I: energy matrix and logos:

       A     C     G     U
0  -328   704   760 -1136
1  2321  1277 -7972  4372
2    31 -3741  1259  2450
3 -4020  1323  1895   801
4  2802 -1139  2384 -4047
5  1632  1399 -4260  1229

I: summed absolute energies of each position:
0     2929
1    15945
2     7483
3     8041
4    10373
5     8520
dtype: int64

I: averaged summed energy over all positions: 8882
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -15213 +/- 6727
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00004 .. 0.04469 (ratio: 1035.1)
I: number of probes: 193055
I: Pearson Correlation  r: 0.4294
I: mean absolute error: 2.6942

I: Classification performance AUROC: 0.9608

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo	r (test)
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed		NaN
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed		NaN
2	best repetition	A2PB1	1000	5	0.627475	0.892899	-14468.149919	False	32.193670	0.002283	0.000071	-1444,..	suppressed		0.382056
3	train dataset	A2PB1	193055	5	0.408764	0.957661	-14468.149919	False	394.225913	0.016499	0.000042	511,..	suppressed		0.409149
4	train, extended	A2PB1	193055	6	0.429464	0.960805	-11634.110305	False	1132.198714	0.012935	0.000011	-330,..	suppressed		0.438725
5	train, expanded, border	A2PB1	193055	7	0.431486	0.960336	-9027.941911	False	1439.405725	0.006122	0.000004	-346,..	suppressed		0.437049
6	manually adjusted G0	A2PB1	193055	7	0.431486	0.960336	-9027.941911	False	1439.405725	0.006122	0.000004	-346,..	suppressed		0.438626

STAGES.df.drop(6, inplace=True)

# store results and display stages
STAGES.append('manually adjusted G0', last_model, new_entries={'r (test)': mf.linregress(last_model.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

	stage	protein	# probes	motif length	r	AUROC	G0	G0 fitted	ratio	max binding	min binding	energies	model	logo	r (test)
0	quick	A2PB1	1000	3	0.361873	0.754115	-21161.022239	False	58.086916	0.066610	0.001147	-2768,..	suppressed		NaN
1	best grid	A2PB1	1000	5	0.469313	0.832928	-14468.149919	False	141.217108	1.618389	0.011460	950,..	suppressed		NaN
2	best repetition	A2PB1	1000	5	0.627475	0.892899	-14468.149919	False	32.193670	0.002283	0.000071	-1444,..	suppressed		0.382056
3	train dataset	A2PB1	193055	5	0.408764	0.957661	-14468.149919	False	394.225913	0.016499	0.000042	511,..	suppressed		0.409149
4	train, extended	A2PB1	193055	6	0.429464	0.960805	-11634.110305	False	1132.198714	0.012935	0.000011	-330,..	suppressed		0.438725
5	train, expanded, border	A2PB1	193055	7	0.431486	0.960336	-9027.941911	False	1439.405725	0.006122	0.000004	-346,..	suppressed		0.437049
6	manually adjusted G0	A2PB1	193055	6	0.429418	0.960814	-15000.000000	False	1035.086607	0.044687	0.000043	-328,..	suppressed		0.438626

STAGES.df.to_json('%s_%s-%s-%s_%s-%s.json' %(PROTEIN_NAME, datetime.now().year, datetime.now().month,datetime.now().day , datetime.now().hour, datetime.now().minute))
STAGES.df.to_pickle('%s_%s-%s-%s_%s-%s.pkl' %(PROTEIN_NAME, datetime.now().year, datetime.now().month,datetime.now().day , datetime.now().hour, datetime.now().minute))